Solving Math Equations but they keep getting HARDER | jensenmath.ca

Welcome to JensenMath! In this video, we'll dive into 11 high school math equations, starting from fundamental algebraic expressions and progressing to more advanced topics like quadratic equations, exponentials, logarithms, and trigonometry. Whether you're a student looking to reinforce your understanding or a curious mind eager to explore the beauty of mathematics, this video is for you!
Throughout the video, we'll provide step-by-step explanations and examples to help you grasp each concept. Remember, math is not just about memorizing formulas; it's about understanding the underlying principles and applying them to solve problems.
For additional resources and practice materials, visit our website at jensenmath.ca. Don't forget to like, comment, and subscribe to JensenMath for more math-related content. Let's explore the fascinating world of mathematics together!
0:00 - level 1 equation
1:06 - level 2 equation
2:22 - level 3 equation
3:33 - level 4 equation
5:14 - level 5 equation
6:08 - level 6 equation
8:33 - level 7 equation
10:55 - level 8 equation
13:57 - level 9 equation
16:43 - level 10 equation
20:55 - level 11 equation

[@Taric25]

I thought you were going to end with complex analysis. These were all pre-calculus.

[@yourcolotisdifferent]

Bro just look up complex analysis problems if you wanted to do them so bad

[@TrustingTroller]

23:16 "Through all 11 difficulties of high school-math-level equations"

[@dickmeatbootysack2165]

@@TrustingTrollerohhhhh he says that at the end of the video where obviously a new viewer will see immediately

[@josephlorizzo8997]

i thought that too bruh

[@rhoclouds]

@@TrustingTroller if this is the highest level of math you reach in high school, then something is wrong. no offense

[@azuarc]

I must not be the target audience for this video because I thought these were all really basic. My pre-calc students should be able to solve all of these. I was waiting to be actually challenged.

[@virajpatil1017]

True😂🎉

[@instinx9154]

then do integration bee questions

[@wallcatpl810]

I mean the target audience is probably algebra 2 students, or precalculus students.

[@Cobydude905]

Maybe yeag

[@arkaprovodas4920]

same

[@janvasicek8843]

I was waiting for differential equations. But this video was awesome to watch, you have a nice voice😊.

[@Booskop.]

I've been out of math class for 15 years and I managed to solve the first 3 equations. Consider me a happy man. Edit: I was glad when you noticed the missing bracket and corrected it.

[@user-fx3bk4md6d]

I'm 15 and solved first 5 questions 😊

[@shreyashpachore4156]

@@user-fx3bk4md6d I am 15 and have taken Calculus 3

[@user-ed8re6eg9p]

8 was able to do first four and more 5:05

[@mukundkumar2483]

​@@user-fx3bk4md6dI'm 16 and solved all of them

[@abdallahbac]

17 and solved all of them With less then 2 secondes each

[@jakejake7958]

I actually really enjoyed this type of video. I am currently in Grade 12 (finished advanced functions) and I was able to get everything correct except for #10 because I forgot the identities. Great vid I really enjoyed this!

[@AMig-ht8nw]

Im grade 3 lolll

[@shubham_sharma777]

​@@AMig-ht8nw not a flex dude

[@sdaeu]

@@AMig-ht8nw What? Why on earth are you solving equations that young. I mean, I can understand the easiest but the complex ones? Ain’t no way 🤣 Get off technology and enjoy your childhood, no need to worry about studying properly into you reach high school, as that is when you will have public examinations.

[@nathanswinford2430]

Yoo same just finished AP Calc BC but I forgot the trig identity

[@Silver_crap]

Basically you solved different kind of quadratic equations...nice👌👌.

[@OculusVeri]

Nice So I paused the video and just ended level 1 after 2 hours of calculating Looking forward for level 2 So far so good

[@davincitoredivinott1508]

Is that the ingushetia flag

[@papapapalima_scotland]

Great practice. Got all but 9 and 10 right. 9 I made a silly mistake, but I own it. 10 I was completely out of my depth, would need a refresher in trig. 1 to 8 and 10 were enjoyable but nothing too difficult.

[@King-sd5vg]

Really cool video, this is great for someone like me who missed out early into math, but I'm really fascinated by it now and trying to learn! I've noticed a lot of the time people do anything in their power to not use the quadratic formula I wonder why? For me it's been 10x easier every time I see a quadratic just throw everything into the formula and most of the time it works out nicely.

[@shubhtiwari8479]

thats because for simpler equations, using the quadratic formula just makes it longer even though its more efficient, but by using the factorisation method (which u can get really good at by practicing) u can solve these type of equations even faster and save a lot of time and energy. And as the great mathematicians say, in order to become great at math, we should become lazy so that we can find easier methods to solve problems😂

[@riccardofroz]

Level 8 I would have done it without "test": x^4-x^3-11x^2+9x+18=0 Split -11x^2 in -2x^2 and -9x^2 and manipulate the signs to have the following (x^4-x^3-2x^2) - (9x^2-9x-18)=0 Factor x^2 on the left parenthesis group and 9 on the right: (x^2-x-2)x^2-9(x^2-x-2)=0 (x^2-9)(x^2-x-2)=0 x=+-3 x=(1+-sqrt(9))/2=-1,2

[@joetsu7109]

i did the same exact thing

[@sushantagarwal720]

Same

[@cariogenic]

just a question how do you know to split the x^2 term into those exact numbers? I usually struggle factoring polynomials of order 3 or greater without the rational root theorem.

[@DadoLMN]

Did the same thing!

[@layer1087]

​@@cariogenic experience and skull development can play a factor in here, I didnt know you could do it like this so I'm kinda happy to learn smng new. I used test all the way ±1, ±2 and ±3 (was just wondering if there are more answer from test or would I have to divide but all the answers were there lol)

[@mrgamepigeon6586]

I struggled massively with the level 6 equation. I did it but I went throught like 20 steps. All that for you to show me that I could've taken the log of both sides.

[@azmard4865]

That's maths for ya brotha o○o

[@aguy5321]

Lol same

[@charlescrawford9972]

Saving this for my 10 year old. He'd love this.

[@Iamsnowedyt]

10 year olds can only the first one

[@w花b]

​@@Iamsnowedytmaybe their kid is the next Terrence Tao

[@TakshabDahal]

​@@Iamsnowedytwhen I was ten I could do up to the 4th one

[@srimattheuniverseshow]

*Yes i can definitely understand level 11 As a 11 y/o*

[@dgnoob18]

​@@Iamsnowedytno

[@JeftherGabriel]

Wow, I didn't know it was possible to factor quadratic expressions in this way. In school, I only learned to use the resolution formula. At least I can handle exponentials and logarithms; I'm not sure about trigonometrics yet.

[@bjornfeuerbacher5514]

Another way to do equation 6: Write it as 4^(3x) times 4^(-1) = 5^x times 5^2, bring every factor with x to the left and every factor with x to the right, so 4^(3x)/5^x = 5^2 times 4, which easily simplifies to (64/5)^x = 100. If you have a modern calculator which can do logs to every basis, now you just have to take the log to the basis 64/5 and you are done; otherwise use log to the basis 10 and use log(64/5)^x = x times log(64/15).

[@tobyndutchess4415]

I simplified with indicies laws then did the log at the end.

[@douglasstrother6584]

Log rolling! Channel your inner Lumberjack! These are all pretty fun.

[@earth3039]

Nostalgic refresher😊

[@inconspicuous45]

As a 9th grader (currently halfway through algebra 2) I was pleasantly surprised that I could do the first 6 with ease

[@vinaymohan.]

Me also but got only 5 right.

[@skittles8186]

same, I got almost all of them right except for that one trig one but I could do #10 once I looked up the Pythagorean identities

[@tanuahuja1102]

I'm in 9th too....I got all of them except the sixth

[@TenguSteel]

It would be wonderful if there were links to deeper instruction into how to solve each type of problem mentioned here.

[@namangupta2214]

All 11 had fun

[@parth_06]

this all was easy, but nice video for problem solving approaches

[@NellvinCervantes-gt4ot]

Calculus (we include Physics to be more fun) Levels: *Level 1 - 4 : Differential Calculus Level 1 - 2 : Related Rates Application (Level 1, more simply for example is calculating the rate of change of length of shadow in time. Level 2, more complex, we include physics like calculating the accelerations of blocks suspended in the pulleys.) Level 3 - 4 : Relative Minima and Maxima Applications (Level 3, for example is calculating the minimum distance travelled by an ant in a pyramid between 2 given points. Level 4, we can include physics like calculating the minimum/maximum force applied to an accelerating body in a system by using newton's 2nd law). *Level 5 - 8 : Integral Calculus Level 5 (from probability, calculating the expectation value of random variable) Level 6 : (evaluate integral dx/(x^11 + 1). Level 7 : application (if we include physics, determine the work done on a long and heavy rope placed on different inclinations of surfaces). Level 8 : derivation (if we include physics, structural theory, Derive the 3-moment equation) *Level 9 - 12 : Differential Equation : Level 9 : application (if we include physics, calculate the angle rotation in terms of time of rigid bar in a given system of springs. The springs one ends attached on ceiling and their other ends attached to the bar). Level 10 : derivation (if we include physics, Electromagnetism, Derive the electric field and magnetic field at a distance from short dipole antenna, by using Maxwell's Equation). Level 11 : derivation (if we include physics, Quantum Mechanics, show that the magnetic quantum number (m_l) is set of integers ranging from negative angular momentum quantum number (-l) to positive angular momentum quantum number (+l) by using Schrodinger Equation). Level 12 : application (if we include physics, General Relativity, Derive the Kerr Metric for rotating and uncharged massive body).

[@bryantwiltrout5492]

It’s been awhile since I took a math course but I remembered quite a bit of these. I got stuck on the last one ngl. Other than that it wasn’t super difficult.

[@electricgamer_yt4753]

The advanced trig way to write equation #7 is: x_1=7π6+2πn | X_2=11π6+2πn Assuming _ means "subscript" and n is an integer. It expresses all of the infinite solutions. Obviously there isn't infinite solutions in-between 0 and 2π, so in a word problem for less advanced trig, then that makes more sense Also, I was about to comment that x=2-√14 undefined, but nevermind

[@FishbirdDD]

Did he not write that as the solution?

[@frendlyleaf6187]

Nice, very fun!

[@epicstar86]

I solved the level 6 equation by using the rules of expontents in which I got x = log base 64/5 of 100 which is approximately 1.806

[@bijipeter1471]

Thank you, sir

[@jinjin1156]

Your amazing teacher🎉

[@ritumammathsclasses8452]

More such videos please!!!

[@tommyliu7020]

Nothing with the lambert w function or complex plane?

[@mikoajszwarocki7343]

I was waiting for differential equations

[@rubennavarrobonanad9439]

Thought this video would have dif. Eqs. It didn't, but still great vid!

[@alberteinstein3612]

I’m an a-level maths student, so I was expecting a-level analysis for the final questions. Nonetheless, this video was a nice refresher of the math concepts that I haven’t studied in a few years

[@arvin390]

As an A-Level Further Maths student, yeah, this was really easy.

[@trevaperes5343]

This must be math heaven for some!

[@pranavmanjunath5368]

Solved eqn 1 to 5 with ease. Couldn't solve eqn 6 as i have no knowledge of logarithms. Level 7 was super easy(I love trigonometry). Tried level 8 solved it after some time. Couldn't do level 9, but solved level 10 pretty easily. On level 11, I got only 1 of the 2 answers, i.e 2.

[@RubyPiec]

I just solved level 4 with the quadratic formula, but woah! That's insane and I didn't know that was possible also level 7 is as far as i got...

[@vigorershagen1022]

I have never seen secant thingy before and just thought it was funny how its cube was the derivative of tanx

[@Mathmaniac-vw9ip]

As a guy who still haven't reached 9th grade, (close though), I am happy to be able to solve upto 10 and as for 11, after learning first few steps, I was able to do the remaining steps to get the answer. So, I was able to do around 10.5/11 of the problems

[@abehankens7456]

im halfway through precalc and i made it up to level 7, thought they were gonna get a lot harder near the end but they werent??

[@BloodySSK]

for the ninth couldn't youjust use exponential to remove the log ? it would be much easier ?

[@RebornKaotic]

it does the same thing as what he did

[@freedomdive1881]

I was only able to get until level 8. Questions involving logarithms and trigonometric identities are still one of my weakness.

[@tobiuzumaki1229]

For lvl 4 won’t it be easier and simpler to solve by the quadratic formula or the perfect square?

[@Briareos1712]

Level 4 seems a lot more complicated to me than just dividing by ten and use the pq-formula (not sure if it's called like that in english, I mean this one: x=-p/2+-sqrt((p/2)^2-q)

[@superorange3698]

Can't you use pq formula for 3?

[@josephbenson606]

Most of em u can

[@emirayth]

yo i failed at the first one im i cooked?

[@pramana47]

yes

[@earth3039]

Depends on ur grade

[@BaconHair6667]

how old are you?

[@VAIBHAVMALHOTRA19]

No you didn’t. As someone who has great experience in math I still couldn’t solve 2 questions from this video. Actually 3 because in the 8th question I became half delulu.

[@xenon9717]

@@VAIBHAVMALHOTRA19 he failed the basic algebra one

[@laurenelisej]

Y no quadratic formula?

[@LEGEND_SPRYZEN]

All done within a minute

[@CaulolProductions]

me at the first 4 questions: why is bro taking the hard routes?

[@Username-cf5ny]

for level four couldn’t you have done the quadratic formula to get 0 or 32?

[@hrn8935]

Why was i expecting the final question to be a partial differential equation or smg

[@josephquinto5812]

I could do anything not involving trig lol. I despised trig so much that I immediately voided it from my brain the minute my final exam was over.

[@user-qz5um1be6c]

i did until lvl 5 but strangely could do lvl 8, 11 and 10 and none of the in betweens

[@henryucha2705]

These are actually very simple i scale through all of them

[@user-ff1fv6ub7c]

I’m 14 and I found all levels but 10 and 11 very easy, the stuff I didn’t get I just haven’t learnt yet.

[@tzbq]

nice I'm 15 and they haven't taught me a lot of this but I got almost everything

[@alexfrozen8987]

Log base 10 writing like lg, isn't it? Or we can just write log without specifying what base it is

[@adityagoyal3491]

log is by default base 10 also ln is by default base e

[@tzbq]

​@@adityagoyal3491 ln *is* base e because its natural log

[@rampalwe9424]

This is very simple for jee students

[@bigbigx2250]

Tbh I think level 8 is, if not the hardest the most time consuming

[@VAIBHAVMALHOTRA19]

True

[@hackwithtechnoboy548]

you forgot to mention that these are most difficult for americans

[@coolspagamingandtech9302]

Indian kids: 😊😅

[@MehulVerma-nm1wd]

Level 11 equation is a cakewalk for me being an 8th grader in India :)

[@yourcolotisdifferent]

i found a better last problem prove or disprove the Riemann hypothesis

[@aditaggarwal3486]

Was waiting for math olympiad type stuff. Never came. Somewhat disappointed, though I'm used to it by now.

[@pista69420]

i guess i wasnt paying attention in math classes since i could solve only first 1 and half way on 2nd maybe i was too scared to ask "teacher how did that work?"

[@cedricharris_t]

Log questions coudnt do and the last one, 8th grade

[@IamExeller]

Why are there no calculus?????? I thought they'd appear on level 8-9

[@luciferplays1797]

I’m in 8th grade and I solved up to the 9th equation but I didn’t know the identity to solve the 10th equation. Still got a ways to go 😁

[@kenseyder]

Level 6 with easy method: (I'll use n instead of x because I have no exponental letter of x on my keboard) 4³ⁿ-¹=5ⁿ+² 4³ⁿ/4=5ⁿ×5² Divide both sides by 4³ⁿ×5² 1/(4×5²)=5ⁿ/4³ⁿ Take the n out (5/64)ⁿ=1/100 n=log5/64 (1/100) n=-2log5/64 (10)

[@pekonipappa9292]

in uni studying Mechanical Engineering. I had a slight idea on how to do these but cant remember any of the calculatikgnmethods. Solve command has ruined me😂

[@svxernova]

i did everything, that's calculus I (which is kinda easy)

[@zacky_boyyt19]

Me At Level 1,2,3: “Too Easy” Me At Level 4: WTF Is Going!?

[@sirmonke8946]

You probably should've introduced product-log in one of them

[@GrifGrey]

i dont know if product log is high school level

[@MrLarkins]

All 10...had fun.

[@bjornfeuerbacher5514]

All 10 of 11? :D

[@NemanjaSo2005]

Expected the last one to be something IMOers would struggle with, but it ended up being standard.

[@DatBoi_TheGudBIAS]

It took some seconds to remind myself Dat tan²x+1=sec²x Basically every trig identity is obtained from the classic sin²x+cos²x=1, with some manipulations. In this case, we divide both sides by cos²x

[@gamingzeraora443]

It's obtained by the Pythagorean theorem actually

[@boysurfs]

@@gamingzeraora443sin^2(x)+cos^2(x)=1 is the pythagorean theorem my guy

[@MrKrupp42]

Heavy that lad

[@marios_-nk4qg]

Do a floor equation

[@studykunal3237]

JEE Aspirant be like: That 11th one got me to use my pen.

[@Arianani]

5:14 what about 2??

[@-Neko_77-]

11:00 Can't you just put it into standard polynomial form and solve it from then?

[@ummekulsummasuma3575]

Got all 11 equations... It was easy-peasy

[@proton..]

no you didnt

[@idlesquadron7283]

@@proton.. It is not unbelievable

[@josephlorizzo8997]

​@@proton..these were pretty Easy, i believe he/She did

[@Avighna]

That’s what I’m saying, this was so easy. Almost all of them were just disguised quadratics.

[@jamesedward9306]

Congratulations Einstein. I'd like the double whopper with cheese and a large fries.

[@azizprv9693]

I am so glad that I did all of them correctly and I am only 17 years old

[@quiladog9302]

Im in algebra one and I can do except for 10. 10 makes my brain hurt. edit: I was initially planning on testing out of geometry, algebra 2, and precalc but it turns out I just cant do that so I will just test out of geometry and algebra 2.

[@ansh6848]

I was able to solve all of them and it barely took me 9 minutes as starting ones are pretty easier that can be solved in mind only.

[@AniketMohan]

These equations are really easy for a 16yo like me bro 😎😎. I solved all of 'em

[@QuietBob]

oh well, 1st one got me gluglu

[@a.b3203]

Didn’t get 8, never had to learn to solve anything like that.

[@bruhnish598]

i thot bro was gonna give us a diff eq lol

[@ShubhGG12]

im in 8th grade and solved the first 5 questions and the 8th, got the first answer for 11th question and came close to the second answer. I havent learned logarithms or trigonometry completely yet so yeah

[@robertlunderwood]

The worst one for me was the quartic. The only outs to that is the rational root theorem to find at least one root.

[@kusumdevi4460]

Me as a 8th grader watching after level 5:👁👄👁

[@milenasovic]

All 11!

[@minophilic6577]

Bruh I didn't expect to fail in 1st, because I got overconfident and messed up to 3 instead of 18.

[@parthyadav6524]

As a jee aspirant I had no difficulty solving any of these🗿

[@awperbhai8275]

could have added maxima minima problems

[@Samiul_007]

These were all easy. But great job

[@ChavoMysterio]

Completing The Square c=(½b)² x²+4x=12 x²+4x+4=12+4 (x+2)²=16 |x+2|=√16 x+2=±4 x+2=4 x=2 ❤ x+2=-4 x=-6 ❤

[@kellyarnold]

Omo I stopped at difficult log rolling … but was able to do the polynomial question…. So where am I at 😅😅😅

[@VAIBHAVMALHOTRA19]

To all the people who are saying all of them are easy, congrats you have successfully done a great job for having superiority complex. Cmon, have some empathy. Not everybody has good math experience like you or not everybody has interest in practicing math like you. Watch this video through a perception of an average student who is just an average in Math.

[@davidmacarol3673]

Pretty easy :)

[@wallcatpl810]

They are easy, but of course I have some problems, like solving it right, but forgetting that domain of logx is from 0 to infinity, or something like that.

[@KrimzyEditz]

As someone in 6th grade my brain malfunctioned after equation 3...

[@berkayylmaz4782]

As a 8th grader, I passed level 3. I really didn't think that I'll reach there.